Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

On the utility of alternative amino acid scripts

In this work we propose the hypothesis that replacing the current system of representing the chemical entities known as amino acids using Latin letters with one of several possible alternative symbolic representations will bring significant benefits to the human construction, modification, and analysis of multiple protein sequence alignments. We propose ways in which this might be done without prescribing the choice of actual scripts used. Specifically we propose and explore three ways to encode amino acid texts using novel symbolic alphabets free from precedents. Primary orthographic encoding is the direct substitution of a new alphabet for the standard, Latin-based amino acid code. Secondary encoding imposes static residue groupings onto the orthography of the alphabet by manipulating the shape and/or orientation of amino acid symbols. Tertiary encoding renders each residue as a composite symbol; each such symbol thus representing several alternative amino acid groupings simultaneously. We also propose that the use of a new group-focussed alphabet will free the colouring of amino acid residues often used as a tool to facilitate the representation or construction of multiple alignments for other purposes, possibly to indicate dynamic properties of an alignment such as position-wise residue conservation.